Using Young's double slit experiment, a monochromatic light of wavelength \(5000\,\mathring A\) produces fringes of fringe width \(0.5 \,mm\). If another monochromatic light of wavelength \(6000\,\mathring A\) is used and the separation between the slits is doubled, then the new fringe width will be ............... \(mm\)

\(\lambda_{1}=5000 \,\mathring A\)

\(\beta_{1}=\frac{ D }{ d }\left(5000 \times 10^{-10}\right)=5 \times 10^{-4} \,m\)......\((I)\)

\(\beta_{2}=\frac{ D }{(2 d )}\left(6000 \times 10^{-10}\right)= x \text { (let) }\).....\((II)\)

Divide \((II)\) and \((I)\)

\(\frac{\beta_{2}}{\beta_{1}}=\frac{3000 \times 10^{-10}}{5000 \times 10^{-10}}=\frac{x}{5 \times 10^{-4}}\)

\(x=3 \times 10^{-4} m \text { or } 0.3 \,mm\)